No the provided kit only work when the power is on, or that is if you use it on a circuit that is always on then the camera will also be always on, but there are no low voltage cut off in the provided kit, those things only come with the 3 wire hard wire kit used for parking mode.
The separate hard wire kit is 3 wires, it have 1 +12V ACC wire, which you could say is the control input, telling the camera to cone on ( if off ) or change to / from parking mode.
The wire that actually power the camera when the hard wire kit is used is the always live +12 V wire, and then of course last you have the shared - 12 V / GND wire.
So as the provided power source only have the 2 wires, this is why you must wire it to a fuse / circuit that are ACC and so only on when your car is on, otherwise the camera will be on and recording all the time and it will run your car battery totally flat, which is very bad for a lead acid car battery's lifetime.
My recommendation is to wire into the fuse box with a add a fuse adapter, which simply put piggyback in a existing fuse / circuit just parallel to it.
So to get one of those you need to figure out what kind of fuse your car use, these are most likely "blade" type fuses called ATO fuses, but they come in a few different shapes.
ATO fuse models.
My personal Suzuki car use the mini type, one thing to tell them apart ( a few are pretty much same size ) is the 2 letgs, some are blunt point some are pointy.
Your car manual might say what fuese your car have, some times there are also a couple of spare ones in the fuse box you can bring to the store to get a add a fuse adapter.
The add a fuse adapters pretty much all look the same no matter what fuse they are fore, they generally look like this.
The fuse in the picture here is the new fuse for the camera, it go in what i call the top slot, for any dashcam a 5 A fuse will be fine.
The lower slot that is where the original fuse go you pulled out to be able to install the add a fuse adapter.
The little piece of wire is where you connect your new stuff ( +12 V )
When installed it look something like this in the fuse box.
In general you want to tap into a higher AMP fuse, but the smallest ones are often 10 A and that will be fine.
What you have to be careful with is to not go for the "mission critical" fuses like the one for airbags and engine management ASO
Things like accessories - heated seats - cabin light . rear window defroster ASO are open game.
Some cars not least new ones have smart electrical circuits in which case installing a 3 wire hard wire kit to get parking guard can be tricky, this is due to the smarts in the wire harness, so a wire that appeared to be always on when you installed the camera are not that after all.
Good thing is the add a fuse adapter are fairly easy to move to a new fuse, just pull the original fuse out of it and put it back here it belong, then pull another fuse put that in the bottom slot off the add a fuse adapter and then put that in the new empty fuse location.
BUT as you just have the 2 wires to deal with, you just have to find and use a ACC fuse that is only on when the car is on, so the dashcam should turn off when you turn off the car, and likewise come on when you turn on the car.
Some circuits in newer cars can have a delay, like you maybe have seen cabin light or headlights being on for a little while after the owner have left & locked the car, so when you have done your install just be sure the camera go on / off as it should, if you are on a always on fuse the camera will be on always too, and that is no good with the provided power supply.
On youtube there are many videos on how to install dashcams ( it is much the same no matter the brand of dashcam or the brand of the car )
There are also videos on how to hard wire dashcams, these guide will probably be for 3 wire hard wire kits for parking guard, as you dont go there all you need is to identify a ACC fuse for your one +12 V wire
Too bad you are on the other side of the world, i am always available for people if they need help installing a dashcam, but that only go for within reasonable distance in Denmark
Of course you also need to figure out where your fuse box is in the car, that is normally in the manual / quick start guide for the car,,,,,, mine is in a horrible place, where you need to be a contortionist and i am a 55 YO stiff old SOB.
A mistake some make is to use a not suited bolt / screw for the -12 V GND connection, but usually there also is a factory GND connection point near the fuse box
Of course you can also spend money on the hard wire kit and not use the parking guard option, but then you just have 1 more wire to deal with and 1 more fuse to find and use.
PS: A cheap 12 V
LED probe / circuit tester from the dollar store are nice to have, i use a dirt cheap one myself, newer cars need LED, older testers just had a regular bulb in them which was fine back then.